The present invention relates to the measurement of physical-chemical properties of macromolecules. More specifically, it pertains to apparatuses and methods for (1) establishing and maintaining macro-ions (e.g., proteins) dissolved in aqueous and other polar solvents at electrophoretic steady state (defined below) under well-characterized conditions and (2) facilitating the precise and quantitative optical interrogation of the macro-ions so maintained. Analyses of the optical records of macro-ions maintained at electrophoretic steady state in accordance with the apparatuses and methods of the present invention can yield one or more physical-chemical properties of the macro-ions including molar diminished charges (defined below), stoichiometries of assembly and association constants of reversibly associating macro-ion systems, and polydispersity parameters of mixtures of homologous macro-ions (e.g., a production run of a synthetic, linear, charge-bearing polymer). The aforesaid analyses are based on electrophoretic steady-state theory, developed by the inventor and described publicly for the first time in this disclosure.
Because the present invention provides for the first time apparatuses and methods for analyzing macro-ions at electrophoretic steady state, there is no directly related prior art with which the present invention can be compared. Thus, prior electrophoretic techniques, as for example the prior techniques of moving boundary electrophoresis and zonal electrophoresis both of which are based on established electrophoretic transport theory, differ fundamentally from the present invention, as do methods and apparatuses of the prior technique of isoelectric focusing.
However, the technique of steady-state electrophoresis--the term referring here and often throughout this disclosure to the technique of measuring physical-chemical properties of macro-ions maintained at electrophoretic steady state in accordance with the apparatuses and methods of the present invention--can be classified with prior analytical techniques employed to make precise measurements of physical-chemical properties of macromolecules maintaind at chemical or quasi-chemical equilibrium. Several of these prior techniques including the techniques of osmotic pressure, light scattering, and equilibrium ultracentrifugation measure one or more of the properties measured by the steady-state electrophoresis technique. This class of techniques is sometimes favorably compared with hydrodynamic techniques, which include the prior electrophoretic transport techniques alluded to above, whose theoretical bases are, in general, more empirical and model-dependent than the theoretical bases of the chemical-quasi/chemical-equilibrium techniques (see for instance, Cantor, C. R., & Schimmel, P. R. (1980), Biological Chemistry, Part II: Techniques for the Study of Biological Structure and Function, San Francisco, CA, W. H. Freeman and Co.)
The prior chemical-equilibrium techniques of osmotic pressure and light scattering have only occasionally been used to characterize reversibly associating macromolecular systems since these techniques make only a single molecular-weight measurement per experiment and the analysis of reversibly associating systems require many molecular-weight estimates over an often large concentration span. Moreover, because each of these prior techniques measures only one molecular-weight moment, neither is appropriate for estimating dispersity parameters of mixtures of homologous macromolecules.
The prior technique of equilibrium ultracentrifugation, however, has often been utilized to analyze both reversibly associating macromolecular systems and mixtures of homologous macromolecules. A single equilibrium ultracentrifugation analysis carried out in the analytical ultracentrifuge generates effective reduced molecular weights over a large interval of macromolecular concentration. Moreover, both the apparent weight- and z-average effective reduced molecular-weight moments can be determined throughout the macromolecular concentration span generated in the analytical ultracentrifuge at sedimentation equilibrium, and under conditions of meniscus depletion, the apparent number-average effective reduced molecular weight can be calculated as well. Generally in equilibrium ultracentrifugation analyses, effective reduced molecular weights are converted to absolute molecular weights by appropriate conversion factors; however, for the purpose of characterizing reversibly associating macromolecular systems and mixtures of homologous macromolecules, effective reduced molecular weights may be employed with substantially equal facility (the relationship between effective reduced and absolute molecular weights in equilibrium ultracentrifugation theory can be found in Yphantis, D. A., Equilibrium Ultracentrifugation of Dilute Solutions, Biochemistry, 3 (1964), 297; see also below). The capacity to measure more than one moment of apparent effective reduced molecular weight makes the prior technique of equilibrium ultracentrifugation particularly suitable for analyzing mixtures of homologous macromolecules; and the large span of macromolecular concentration over which effective reduced molecular weights may be measured in one analysis especially lends the prior technique of equilibrium ultracentrifugation to the study of reversibly associating macromolecular systems.
The prior theory of equilibrium ultracentrifugation has many formal parallels with the theory of steady-state electrophoresis upon which the methods and designs of the apparatuses of the present invention are based (see below). In addition, the measurements made by the prior technique of equilibrium ultracentrifugation and the technique of steady-state electrophoresis overlap to a large degree. Accordingly, the technique of steady-state electrophoresis possesses many of the advantages associated with the prior technique of equilibrium ultracentrifugation enumerated above. Thus, although electrophoretic, the technique of steady-state electrophoresis is most similar to the prior technique of equilibrium ultracentrifugation, and the methods and apparatuses of the prior technique of equilibrium ultracentrifugation are the prior art with which the present invention is most appropriately compared.
Despite many favorable features, however, the prior technique of equilibrium ultracentrifugation suffers from a number of disadvantages which relate primarily to technical and practical limitations of the analytical ultracentrifuge in which equilibrium ultracentrifugation analyses are performed. Several principal disadvantages of the analytical ultracentrifuge (as exemplified by the Model E Analytical Ultracentrifuge, Beckman Instruments, Palo Alto, CA) relate to the inherent technical difficulties of measuring macromolecular concentration gradients stabilized at sedimentation equilibrium: First, the cells containing stabilized macromolecular concentration gradients at sedimentation equilibrium are fitted to a spinning rotor; consequently, the cells are aligned only for a small fraction of the time in the instrument's optical systems. The resultant low light levels create unfavorable signal-to-noise ratios in the images of the macromolecular concentration gradients recorded by the absorption system. In addition, despite the employment of powerful light sources (including lasers in some custom installations) in the Rayleigh interference optical system, a highly sensitive ("grainy") photographic emulsion is required to record interferograms of the gradients; this high sensitivity is gained at the expense of optical resolving power.
Second, most studies by the prior technique of equilibrium ultracentrifugation are conducted at rotor speeds which cause significant optical distortions in the cell windows, even when sapphire windows (intended for high rotor speeds) are used. These distortions can create optical transmission irregularities, especially at the low wavelengths often used with the absorption optical system; they can also cause reductions in the clarity and warping of Rayleigh interferograms. Moreover, optical defects introduced into the cell windows during equilibrium ultracentrifugation analyses of macromolecules are not always precisely duplicated in the solvent (blank) analyses, which by subtraction are designed to eliminate the effects of distortions in the optical systems during the processing of equilibrium ultracentrifugation data.
Third, Rayleigh interference patterns (interferograms) are produced in the ultracentrifuge only when the two cell-window slits of the cell in the spinning rotor align with the two slits of the double-slit interference mask; during each revolution of the rotor, however, each cell-window slit is aligned once with the "wrong" slit of the interference mask resulting in undiffracted light superimposing on the interference patterns. This contaminating light (approximately half of the light reaching the photographic plate) significantly reduces the contrast and clarity of the interferograms. The contaminating light and the "graininess" of the photographic image discussed above have been contributing factors to the only marginal success to date of incorporating advanced techniques into the analysis of Rayleigh interferograms generated in the analytical ultracentrifuge (e.g., by the application of automated image-analysis techniques in the recording of interferograms). Consequently, photographic records of interferograms are routinely measured manually on an optical micro-comparator; even when the micro-comparator is equipped to automatically transmit the x-y coordinates of interferograms to a computer, the complete analysis of the data from a typical equilibrium ultracentrifugation experiment can consume several hours.
Most importantly, these aforesaid factors which reduce the capacities of the optical systems of the analytical ultracentrifuge to faithfully record concentration gradients in cells at sedimentation equilibrium introduce often unacceptable levels of random and instrumental error into the data. The result has been failure in attempts to unambiguously characterize several reversibly self-associating protein systems by the prior technique of equilibrium ultracentrifugation and the generation of undesirably low confidence levels in the estimates of polydispersity parameters of mixtures of homologous macromolecules.
The analytical ultracentrifuge possesses other disadvantages of a more practical nature. Its physical dimensions require a large area of often scarce laboratory space; its weight and sensitivity to external vibrations require it to be supported on a stable, heavy-load-bearing floor. Several features make the instrument hazardous to use: for instance, the high-voltage, water-cooled light source of the Rayleigh interference optical system presents a major electrical shock hazard, and when operated at high speeds, the heavy titanium rotors often employed in the instrument possess sufficient kinetic energy to break through the steel barrier which surrounds the rotor chamber if the drive motor, drive shaft, or rotor, itself, should fail.
A principal disadvantage of the analytical ultracentrifuge is its initial price and the cost of maintenance, parts replacement, and repair, which are among the highest for a commercial, widely marketed instrument. The high initial price reflects the materials and design requirements of a device which must withstand large physical stresses, and the high maintenance, repair, and parts-replacement costs are a consequence of the wear and fatigue which these stresses impose on many components. For an analytical ultracentrifuge in routine use, the rotor drive is replaced as frequently as twice a year; cells exposed to high rotor speeds can fail after several months.
The molar diminished charge is one property of macro-ions measured in the apparatuses of the present invention by the technique of steady-state electrophoresis which can not be measured by any prior chemical-/quasichemical-equilibrium technique, including the prior technique of equilibrium ultracentrifugation. This property--which can be defined approximately as the apparent (decreased) charge carried by an ion as a result of interactions between it and other ions present in solution--is a quantity of particular interest to the polyelectrolyte chemist. Currently, molar diminished charges of macro-ions are estimated by prior electrophoretic transport techniques, including the prior technique of moving boundary electrophoresis. However, these prior techniques are only capable of estimating molar diminished charges of macro-ions whose frictional coefficients have been experimentally established (sometimes a difficult procedure) or calculated on the basis of assumptions concerning the shapes and sizes of the macro-ions.